The present invention relates to an improved method and apparatus for measuring the viscosity of fluids while flowing on-line in an industrial process.
Viscometers of many different configurations are presently used to measure the viscosity of fluids. Common among these viscometers are capillary type devices. In capillary viscometers fluid is usually accelerated by an external pressure to flow from a reservoir through a capillary and then to exit to air. For Newtonian fluids, the well known Navier-Stokes equations can be used to directly derive the Hagen-Poiseuille equation to determine viscosity: EQU .mu.=(.pi..DELTA.pR.sup.4)/(8.DELTA.LQ)
where R is pipe diameter, Q is volumetric flow rate, .DELTA.p is pressure differential, and .DELTA.L is a length over which pressure differential is measured. This equation derives fluid viscosity from the pressure drop that occurs within a fluid body as it flows through a cylindrical tube. Application of the Hagen-Poiseuille equation, however, is limited to laminar flows (Reynolds numbers of less than 2100), and assumes steady, fully developed, undisturbed and unidirectional flow through a level tube of uniform diameter. One must also consider whether the fluid is Newtonian or non-Newtonian.
In terms of rheological behavior, fluids may be classified as Newtonian or non-Newtonian. Newtonian fluids have a viscosity which is constant regardless of the shear rate applied to the fluid, whereas for non-Newtonian fluids viscosity may vary as shear stress changes.
An acceptable model in which to describe shear sensitive behavior of non-Newtonian fluids is to treat them as "power law" fluids, whose viscosity within a specified operating range is approximated by a power law equation: EQU .mu.=ky.sup.n-1
where .mu. is fluid viscosity, y is a shear rate and k and n are power law constants. For these fluids, the shear rate dependent viscosity at the pipe wall can be solved for using (for purposes of this application this equation will be referred to as "Equation A"): EQU .mu.=K(.DELTA.P/Q)(4n/(3n+1)) (Equation A)
where n is the power law index, and K=(.pi.R.sup.4 /8.DELTA.L) is a constant. This equation, as with the Hagen-Poiseuille equation for Newtonian fluids, assumes steady, fully developed, undisturbed and unidirectional flow through a level tube of uniform diameter.
Prior art capillary viscometers measure fluid flow rate and the pressure drop occurring as the fluid flows a known distance. Because of the configuration of these prior art capillary viscometer configurations, however, the fluid undergoes contraction when it enters the measurement tube and expansion when it exits the measurement tube ("entrance and exit effects"). Also, other flow disturbances can occur through the measuring section of these prior configurations. These factors may result in fluid flow which may be unsteady, not fully developed, and may not be unidirectional through the measuring section. Thus the underlying assumptions of the Hagen-Poiseuille equation and Equation A may be violated.
In order to accurately apply these equations to these prior art capillary viscometers, a .DELTA.L equal to the distance that steady, unidirectional, and fully developed flow occurs would need to be known. This .DELTA.L may not actually be equal to the nominal measured length of the capillary measurement section (a constant), but will instead be an unknown shorter length within the capillary over which steady, fully developed flow occurs. This .DELTA.L will depend on the flow rate, making it a flow dependent variable, and is difficult to determine. The .DELTA.p used in the Hagen Poiseuille equation and Equation A will also of course vary with differing .DELTA.L's, further complicating accurate application of the equations to prior art capillary viscometers.
These problems in the past have been addressed by introducing complicated correction formulae to approximate for entrance and exit effects, so that the .DELTA.L nominal length of the viscometer measurement section may be used. These formulae can be difficult and time consuming to apply, may introduce uncertainty to viscosity determination, and are flow rate dependent, requiring that they be evaluated and reapplied for each given flow rate.
Many industrial processes require an accurate measurement of a process fluid's viscosity. In the paper making and coating industry, for instance, the viscosity of a coating suspension will affect the ability to effectively apply the coating suspension to a base sheet, as well as affecting the weight and quality of the resultant dried coating layer. The viscosity of the fluid in this example is therefore a required process parameter. In this example, as in many others, the viscosity of the fluid will be somewhat dynamic, changing with time and operation conditions, such as flow rate. It is therefore desirable to achieve a continuous reading of the fluid viscosity, preferably while it is "on line" in the process stream.
Because of its scale, the general capillary viscometer configuration does not lend itself well to these industrial applications that require an on-line viscosity measurement in processes which generally use standard pipe sizes of a much larger than capillary scale. For these industrial on-line viscometer applications, a process flow is typically diverted through a section of piping configured specifically to measure viscosity. The configuration is typically similar to that of the above described capillary viscometer, except that it is in a larger scale. The flow may be diverted and regulated by use of a pump or other means, and a measuring section of piping is often configured with a flow meter and pressure measuring instrumentation.
In addition to some of the problems discussed above associated with a capillary viscometer configuration, this larger scale on-line configuration may introduce various additional problems to application of either the Hagen-Poiseuille equation or Equation A. Because the fluid diversion is inherently intrusive to the flow, the diverted flow is often disturbed. Also, the pumping of the fluid, as well as the presence of a flow meter, may further introduce flow disturbances and unsteadiness. Some devices used to measure flow rate, e.g., gear pumps, may also have leakage, leading to error in flow rate measurements.
Others have attempted to address some of these problems. Specifically, it is known to place a Coriolis mass flow meter, equipped with a differential pressure transducer, directly in the process flowpath. The differential pressure transducer measures the pressure drop between a point upstream of the meter and a point downstream of the meter, the distance between points being a known constant. This configuration has the advantage of the flow remaining in the process line. But, because of the looped configuration of a Coriolis meter, this viscometer configuration introduces flow disturbances, leading to violations of the assumptions underlying the equations. Also, this improved configuration does not address the entrance and exit effects that occur as flow enters and exits the measurement section. These disturbances and effects lead to fluid flow in the measurement section that is not fully developed and uni-directional. This results in further inaccuracies in the application of Equation A and the Hagen-Poiseuille equation. The effective .DELTA.L to be used in these equations will not be equal to the distance between pressure measuring points, but will instead need to be experimentally determined for different fluids and flow rates.
There is therefor an unresolved need in industry for an on-line viscometer which features a flow path that avoids entrance and exit effects, and that provides for undisturbed, fully developed, and unidirectional fluid flow. Such a viscometer will allow for more accurate application of the Hagen-Poiseuille expression and Equation A.